Dynamics of vacuum states for one-dimensional full compressible Navier-Stokes equations

Ben Duan; Zhen Luo

doi:10.3934/cpaa.2013.12.2543

Article Contents

2013, Volume 12, Issue 6: 2543-2564. Doi: 10.3934/cpaa.2013.12.2543

This issue Previous Article Local uniqueness of steady spherical transonic shock-fronts for the three--dimensional full Euler equations Next Article Weighted Sobolev-Hardy spaces and sign-changing solutions of degenerate elliptic equation

Dynamics of vacuum states for one-dimensional full compressible Navier-Stokes equations

Ben Duan^1, and
Zhen Luo^2,

1.
Pohang Mathematics Institute, Pohang University of Science and Technology, Pohang, Kyungbuk 790-784
2.
School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005

Received: June 2012

Revised: March 2013

Published: November 2013

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Abstract

In this paper, we consider the properties of the vacuum states for weak solutions to one-dimensional full compressible Navier-Stokes system with viscosity and heat conductivities for general equation of states. Under weak conditions on initial data, we prove that if there is no vacuum initially then the vacuum states do not occur in a finite time. In particular, the temperature variation has no immediate effects on the formation of the vacuum. There are no assumptions on density in large sets. Furthermore, we prove that two initially non interacting vacuum regions will never touch in the future.

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Mathematics Subject Classification: 35Q30, 35Q35, 76N15.}.

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